where “\(\langle \cdots \rangle \) ” means average over different
realizations of the noise terms in Eq. (REF ) (see, for
instance
Refs. [1]}, [2]}, [3]} for
details of the numerical procedure). Given an appropriate gauge,
\({\cal R}\)  is composed of contributions from the inflaton momentum
perturbations \(\Psi _\phi = -c_{s}^{-1}\dot{\phi }\delta \phi \)  and from
the radiation momentum perturbations \(\Psi _r\) ,
\(&&{\cal R}= \sum _{i=\phi ,r} \frac{\rho _i + p_i}{\rho +p}{\cal R}_i\;,\\&&{\cal R}_i = -\varphi - \frac{H}{\rho _i + p_i} \Psi _i\,,\) 
